Platonic and Archimedean Solids

This is a intended to be a steady stream of cool ideas about Platonic and Archimedean Solids.

**Page under construction**

It Starts with the Tetrahedron

The tetrahedron is awesome. It has 4 triangles for faces, 4 vertices, and 6 edges. A vertex is a point (0-dimensional). An edge is a segment (1-D). A face is a polygon (a 2-dimensional enclosed shape with segments for sides). Put them all together and you get the tetrahedron, which is 3-dimensional. Here’s a video (click YouTube or Full Screen to enlarge):

The dual of the tetrahedron is itself! (as shown in the video).

We will see that the tetrahedron appears in and around the other Platonic and Archimedean solids.

The Platonic Solids

A Platonic solid is a regular, convex polyhedron with congruent faces of regular polygons (meaning all sides and all angles are the same) and the same number of faces meeting at each vertex.

It can be shown that the only possible faces are (regular) triangles, squares, and pentagons. You might think about what might go wrong if you tried to have 3 hexagons meet at a point.

It is fairly easy to see that there are only five possible Platonic solids. They are the tetrahedron, cube (or hexahedron), octahedron, dodecahedron, and icosahedron.

Here’s four more videos, if you didn’t view them all above (click YouTube or Full Screen to enlarge):